In a communication network, instantaneous channel state information (CSI) is required at the receiver for coherent detection. In practice, to achieve this, the transmitter sends a pilot signal including pilot tones, which are predetermined and known at the receiver. Then, the receiver estimates the CSI based on the received signal.
In OFDM, Pilot Symbol Assisted Modulation (PSAM) can be used to estimate the CSI, where the pilot tones are inserted over sub-carriers. Partial or entire sub-carriers can be assigned to the pilot tones. More pilot tones improve the accuracy of the CSI. However, the pilot tones consume bandwidth and decrease the effective data rate.
Due to the multipath, wireless channel have a random fluctuation in the frequency domain, which makes the channel frequency selective. In addition, mobility can result in the Doppler effect, so the channel becomes time-varying. With the combinations of the multipath and time-variations, the wireless channel becomes doubly selective with fluctuations in both time and frequency domains.
One way to estimate a doubly selective channel is to insert the pilot tones in the time and the frequency domains. Then, one can construct a two-dimensional filter as the CSI estimator that processes the pilot tones in time and frequency. However, this requires a high computational complexity and an additional processing delay.
The number of pilot tones that are inserted can be related to the channel selectivity in the time and frequency domains. If the channel has a high selectivity in frequency domain, more pilot tone can be assigned in the frequency domain. In a same way, for a time-varying channel, more the pilot tones can be assigned in the time domain.
In practice, a block-type pilot tone assignment, where all sub-carriers of specific OFDM symbol are allocated to the pilot tones, is useful for a slow-fading and frequency-selective channel. In contrast, comb-type pilot assignment, where the specific sub-carriers (frequencies) are assigned to the pilot tones, is appropriate for the fast fading channel.
Channel estimation can be performed in the frequency domain as well as in the time domain. In the frequency domain, a channel frequency response (CFR) is estimated. In the time domain, a channel impulse response (CIR) is estimated, where the channel frequency response is found by a discrete Fourier transform of the CIR.